Well for me the exchanges made me do the kyc and that only did take less then a day. And yes it was only some little information nothing so personal.
If the exchanges would ask me for more verification then I will trade my coins on a other exchange. I do not want them to make a reason to take my coins or ask for more verification.
Although the time for verification approval from one exchange differs because they're mostly verified if the document provided meet the visibility they wanted but if not they might take time to verify or give you a respond, although sometimes there respond can be very fast especially when those documents are not the standard document for there verification, there are times before 30 minutes you have been verified but sometimes 24 hours. However if an exchange has different step of verification they would show you were it will be very visible but if nothing of that is on there exchange other than the only one they require I don't think is right for them to ask for more on the future if there was no announcement for that.